Séminaires : Séminaire Géométrie et Topologie

Equipe(s) : aa, acg,
Responsables :P.-A. Guihéneuf, V. Humilière, B. Petri, A. Sambarino
Email des responsables :
Salle : 15-25-502
Adresse :Campus Pierre et Marie Curie

Ce séminaire s’adresse aux géomètres, topologues et dynamiciens au sens large. Il est rattaché aux équipes Analyse Algébrique et Analyse Complexe et Géométrie. Les exposés seront accessibles à une audience large, doctorants inclus. Il se tiendra à Jussieu, le jeudi à 11h, en salle 15-25 502. Le séminaire a l'agenda google suivante: https://calendar.google.com/calendar/b/0?cid=dDgzNTJoczNmdDhlMm5nb2IzMXJwaWpsdHNAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ

Orateur(s) A. Sanders - Heidelberg,
Titre G-opers and the holonomy map
Horaire11:00 à 12:00
Résume The main goal of the talk will be to draw parallels between the theory of complex projective structures on Riemann surfaces, and the theory of opers. We plan to define all of the relevant notions, and the talk should be accessible to anyone with a background in Riemann surface theory and some familiarity with Lie groups and homogeneous spaces.

To wit, given a complex semisimple Lie group G and a compact Riemann surface X, a G-oper on X is a gauge theoretic generalization of the notion of a complex projective structure on X, with the notions coinciding when G is the group of projective linear transformations of the complex projective line. In this talk, we will prove some basic structure theorems about the deformation space of marked G-opers. In particular, we will prove that this space is a complex analytic manifold which is a holomorphic fiber bundle over Teichmuller space. Furthermore, we will generalize a theorem of Hejhal and Hubbard (which states that the holonomy map from the space of complex projective structures to the space of flat PSL(2,C)-bundles is a local biholomorphism) to the setting of G-opers. As a consequence, we show that the space of G-opers admits a constant rank holomorphic differential two form, and discuss the relationship with the (pre)-symplectic geometry of the bundle of pluri-canonical sections over Teichmuller space.
AdresseCampus Pierre et Marie Curie